Abstract
The properties of low-frequency global seismic noise, represented by continuous records for 24 years, 1997–2020, are investigated at 229 broadband stations located around the world. The property of waveforms, known as the Donoho–Johnston threshold, which separates the absolute values of the orthogonal wavelet coefficients into "small" and "large" is analyzed. The ratio of the number of "large" coefficients to their total number is determined by the dimensionless DJ index, which takes values from 0 to 1. The DJ index is considered as a measure of the nonstationarity of noise: the larger is the DJ index, the more is nonstationary the waveform. For each station, daily DJ index values are calculated. An auxiliary network of 50 reference points is introduced, the positions of which are determined by clustering the positions of seismic stations. For each reference point, a time series is constructed with a time step of 1 day, which is calculated as the median of daily DJ index values from the 5 nearest operable stations. For all pairs of reference points, the coherence between the DJ index values is estimated in a sliding time window of 365 days with an offset of 3 days, and the maximum values of the coherence function and the frequency at which the maximum coherence is reached are determined. The average values of the maximum coherences show strong growth after 2003, and the maximum distances between the reference points, for which the maximum coherence exceeded the threshold of 0.9, undergo an explosive increase in values after 2012. By extrapolating and averaging the DJ index values at the reference points, the region of concentration of maximum DJ index values was determined at the North-East Siberia. The bursts in the mean value of the maximum coherences between the day length and the DJ index values at the control points precede the release of seismic energy with a delay of about 530 days.
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References
Ardhuin, F., Stutzmann, E., Schimmel, M., & Mangeney, A. (2011). Ocean wave sources of seismic noise. Journal of Geophysical Research, 116, C09004.
Aster, R., McNamara, D., & Bromirski, P. (2008). Multidecadal climate induced variability in microseisms. Seismological Research Letters, 79, 194–202.
Bendick, R., & Bilham, R. (2017). Do weak global stresses synchronize earthquakes? Geophysical Research Letters, 44, 8320–8327. https://doi.org/10.1002/2017GL074934
Costa, M., Goldberger, A. L., & Peng, C.-K. (2005). Multiscale entropy analysis of biological signals. Physical Review E, 71, 021906.
Costa, M., Peng, C.-K., Goldberger, A. L., & Hausdorf, J. M. (2003). Multiscale entropy analysis of human gait dynamics. Physica A: Statistical Mechanics and Its Applications, 330, 53–60.
Donoho, D.L., & Johnstone, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association, 90(432), 1200–1224. http://statweb.stanford.edu/~imj/WEBLIST/1995/ausws.pdf
Duda, R. O., Hart, P. E., & Stork, D. G. (2000). Pattern Classification. Wiley-Interscience Publication.
Huber, P.J., & Ronchetti, E.M. (2009). Robust Statistics, 2nd edn. Wiley. https://doi.org/10.1002/9780470434697.ch1
Kedar, S., Longuet-Higgins, M., Webb, F., Graham, N., Clayton, R., & Jones, C. (2008). The origin of deep ocean microseisms in the North Atlantic Ocean. Proceedings of the Royal Society A, 464, 777–793.
Kobayashi, N., & Nishida, K. (1998). Continuous excitation of planetary free oscillations by atmospheric disturbances. Nature, 395, 357–360.
Koutalonis, I., & Vallianatos, F. (2017). Evidence of non-extensivity in earth’s ambient noise. Pure and Applied Geophysics., 174, 4369–4378. https://doi.org/10.1007/s00024-017-1669-9
Levin, B. W., Sasorova, E. V., Steblov, G. M., Domanski, A. V., Prytkov, A. S., & Tsyba, E. N. (2017). Variations of the Earth’s rotation rate and cyclic processes in geodynamics. Geodesy and Geodynamics, 8(3), 206–212. https://doi.org/10.1016/j.geog.2017.03.007
Lyubushin A. (2018). Synchronization of geophysical fields fluctuations. In: Complexity of Seismic Time Series: Measurement and Applications, Editors: Tamaz Chelidze, Luciano Telesca, Filippos Vallianatos, Elsevier 2018, Amsterdam, Oxford, Cambridge. Chapter 6, pp 161–197. https://doi.org/10.1016/B978-0-12-813138-1.00006-7
Lyubushin, A. A. (2014). Analysis of coherence in global seismic noise for 1997–2012. Izvestiya, Physics of the Solid Earth, 50(3), 325–333. https://doi.org/10.1134/S1069351314030069
Lyubushin, A. A. (2015). Wavelet-based coherence measures of global seismic noise properties. Journal of Seismology, 19(2), 329–340. https://doi.org/10.1007/s10950-014-9468-6
Lyubushin, A. A. (2017). Long-range coherence between seismic noise properties in Japan and California before and after Tohoku mega-earthquake. Acta Geodaetica Et Geophysica, 52, 467–478. https://doi.org/10.1007/s40328-016-0181-5
Lyubushin, A. (2020a). Trends of global seismic noise properties in connection to irregularity of earth’s rotation. Pure and Applied Geophysics., 177, 621–636. https://doi.org/10.1007/s00024-019-02331-z
Lyubushin, A. (2020b). Connection of seismic noise properties in japan and california with irregularity of earth’s rotation. Pure and Applied Geophysics., 177, 4677–4689. https://doi.org/10.1007/s00024-020-02526-9
Lyubushin, A. (2020c). Global seismic noise entropy. Frontiers in Earth Science, 8, 611663. https://doi.org/10.3389/feart.2020.611663
Lyubushin, A. A. (2021a). Seismic noise wavelet-based entropy in Southern California. Journal of Seismology, 25, 25–39. https://doi.org/10.1007/s10950-020-09950-3
Lyubushin, A. (2021b). Low-frequency seismic noise properties in the Japanese Islands. Entropy, 23, 474. https://doi.org/10.3390/e23040474
Lyubushin, A. A., Kopylova, G. N., & Serafimova, Yu. K. (2021). The relationship between multifractal and entropy properties of seismic noise in Kamchatka and irregularity of the earth’s rotation. Izvestiya, Physics of the Solid Earth, 57(2), 279–288. https://doi.org/10.1134/S106935132102004X
Mallat, S. (1999). A Wavelet Tour of Signal Processing (2nd ed.). Academic Press.
Marple (Jr), S. L. (1987). Digital Spectral Analysis with Applications. Prentice-Hall Inc.
Nishida, K., Kawakatsu, H., Fukao, Y., & Obara, K. (2008). Background love and Rayleigh waves simultaneously generated at the Pacific Ocean floors. Geophysical Research Letters, 35, L16307.
Nishida, K., Montagner, J., & Kawakatsu, H. (2009). Global surface wave tomography using seismic hum. Science, 326(5949), 112.
Rhie, J., & Romanowicz, B. (2004). Excitation of Earth’s continuous free oscillations by atmosphere-ocean-seafloor coupling. Nature, 431, 552–554.
Shanker, D., Kapur, N., & Singh, V. (2001). On the spatio temporal distribution of global seismicity and rotation of the Earth—A review. Acta Geodaetica Et Geophysica Hungarica., 36, 175–187. https://doi.org/10.1556/AGeod.36.2001.2.5
Tanimoto, T. (2001). Continuous free oscillations: Atmosphere-solid earth coupling. Annual Review of Earth and Planetary Sciences, 29, 563–584.
Tanimoto, T. (2005). The oceanic excitation hypothesis for the continuous oscillations of the Earth. Geophysical Journal International, 160, 276–288.
Vallianatos, F., Koutalonis, I., & Chatzopoulos, G. (2019). Evidence of Tsallis entropy signature on medicane induced ambient seismic signals. Physica A: Statistical Mechanics and Its Applications, 520, 35–43. https://doi.org/10.1016/j.physa.2018.12.045
Varotsos, P.A., Sarlis, N.V., & Skordas, E.S. (2011). Natural time analysis: the new view of time. In: Precursory Seismic Electric Signals, Earthquakes and other Complex Time Series. Springer-Verlag Berlin Heidelberghttps://doi.org/10.1007/978-3-642-16449-1
Varotsos, P. A., Sarlis, N. V., & Skordas, E. S. (2003a). Long-range correlations in the electric signals that precede rupture: Further investigations. Physical Review E., 67, 021109. https://doi.org/10.1103/PhysRevE.67.021109
Varotsos, P. A., Sarlis, N. V., & Skordas, E. S. (2003b). Attempt to distinguish electric signals of a dichotomous nature. Physical Review E., 68, 031106. https://doi.org/10.1103/PhysRevE.68.031106
Varotsos, P. A., Sarlis, N. V., Skordas, E. S., & Lazaridou, M. S. (2004). Entropy in the natural time domain. Physical Review E, 70, 011106. https://doi.org/10.1103/PhysRevE.70.011106
Xu, C., & Sun, W. (2012). Co-seismic Earth’s rotation change caused by the 2012 Sumatra earthquake. Geodesy and Geodynamics, 3(4), 28–31. https://doi.org/10.3724/SP.J.1246.2012.00028
Zotov, L., Sidorenkov, N. S., Bizouard, C., Shum, C. K., & Shen, W. (2017). Multichannel singular spectrum analysis of the axial atmospheric angular momentum. Geodesy and Geodynamics, 8(6), 433–442. https://doi.org/10.1016/j.geog.2017.02.010
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The work was carried out within the framework of the state assignment of the Institute of Physics of the Earth of the Russian Academy of Sciences (topic AAAA-A19-119082190042-5)
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Lyubushin, A. Global Seismic Noise Wavelet-based Measure of Nonstationarity. Pure Appl. Geophys. 178, 3397–3413 (2021). https://doi.org/10.1007/s00024-021-02850-8
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DOI: https://doi.org/10.1007/s00024-021-02850-8